Question

You are given the following information about two computer software firms and the S&P Industrials:

	Company A	Company B	S&P Industrials
P/E ratio	30.00	28.00	17.00
Expected annual growth rate	0.17	0.14	0.07
Dividend yield	0.00	0.01	0.02

a. Compute the growth duration of each company stock relative to the S&P Industrials. Do not round intermediate calculations. Round your answers to two decimal places.

Company A: _____ years

Company B: _____ years

b. Compute the growth duration of Company A relative to Company B. Do not round intermediate calculations. Round your answer to two decimal places.

_____ years

Answer 1

As per Growth Duration Model,

In(PEc/PEb)= T*In[(1+Gc+Dc)/(1+Gb+Db)]

Where

PEc= PE of company assessed. PEb = PE of Benchmark

T= Growth Duration

Gc= Growth rate of company, Gb= Growth rate of benchmark

Dc= Dividend yield of company and Db= Dividend yield of benchmark.

Given, PE of Company A=30, PE of Company B=28, PE of S&P Industrials=17

Expected Annual Growth rate of A=0.17, of B=0.14 and of S&P Industrials=0.07

Dividend yield of A=0, B= 0.01 and S&P Industrials=0.02

(a)   Substituting the values for Company A relative to S&P industrials,

In (30/17)= T*In[(1+0.17+0)/(1+0.07+0.02)

In (30/17) = T* In(1.17/1.09)

In (1.76470588)= T* In(1.073394495)

0.567984036 = T* 0.070826052

Therefore, Growth Duration of Company A relative to S&P Industrials (T)= 0.567984036/0.070826052 = 8.02 years

Substituting the values for Company B relative to S&P industrials,

In (28/17)= T*In[(1+0.14+0.01)/(1+0.07+0.02)

In (28/17) = T* In(1.15/1.09)

In (1.647058824) = T*In(1.055045872)

0.498991166 = T* 0.053584246

Therefore, Growth Duration of Company B relative to S&P Industrials (T)= 0.498991166/0.053584246 =9.31 years

(b) Substituting the values for Company A relative to Company B,

In (30/28)= T*In[(1+0.17+0)/(1+0.14+0.01)

In (30/28) = T* In(1.17/1.15)

In (1.071428571 = T* In(1.017391304)

0.068992871 = T*0.017241806

Therefore, Growth Duration of Company A relative to Company B (T)=0.068992871/0.017241806 =4 Years